A domain is all or a portion of the tactile surface of a physical object or discrete entity having at the minimum two dimensional boundaries and dedicated to selection by humans to effect command. In this case, to command the production of musical tones. The two dimensional boundaries of the domains may lie in a curved two dimensional space following the surface shape of the underlying object or entity. Examples would be a typical computer screen or along the user contacted tops of traditional three dimensional fingerkeys. Domains in conjunction with a plurality of other similar domains create zones of common influence termed either contiguous domains or broken domains.
Contiguous domains are a directional stream (in this case a horizontal stream) of like domains aligned in the same general plane allowing by sequential selection a sounding of a recognized grouping of tones. In the preferred embodiment of this invention, this recognized grouping is a series of wholetones, which are commonly expressed in the art as a collection of tones that are 200 cents apart.
Broken domains are also a directional stream (also in this case a horizontal stream) of like domains aligned in the same general plane, but only offering by individual (not sequential) selection a recognized grouping of tones. The sequential selection is denied by other structure passing through and impeding the general plane holding the broken domains. As a further understanding of this, a study of the common keyboard (FIG. 6A) is warranted, as it clearly illustrates both contiguous and broken domains.
The front ends of the seven per octave white keys are contiguous domains. In FIG. 6A the frontal domain of the B fingerkey is designated as 41. Posterior to these contiguous domains is a region collectively termed the intrusion zone. The back domain 40 of the B fingerkey forms with the other back domains a broken domain zone. Rising (intruding) between most of them are the five shortened black fingerkeys such as Bb 39. The latter are uniformly elevated to have their upper surfaces also form contiguous domains. This is true because in the plane containing these elevated domains, there is no impeding of direct lateral movement by the musician.
Because they are freely accessed in a common plane, both the back keys and the anterior portions of the white front keys form contiguous domains and allow glissandos. In and amongst themselves, the posterior portions of the white keys do not allow glissandos. A glissando is an operator maneuver whereby a digit is run rapidly over a minimum of three laterally aligned domains to create a desirable musical effect.
From the perspective of the musician, the rear keys are collectively accessible to the fingers for individual selection or for pentatonic glissandos mainly in the key signatures of E flat minor and G flat major. The anterior portions of the front keys are collectively accessible for individual selection or for diatonic glissandos mainly in the key signatures of C major and A minor. And the posterior portions of the front keys are only accessible as broken domains providing individual selection only.
The most obvious characteristic of this common layout is the fact it is by definition an irregular system. The grouping of tones triggered by either form of glissando does not increment by uniform intervals and hence limits their usefulness in almost all the key signatures except a select few. If employed in the nonselect majority of key signatures, these glissandos tend to sound from slightly disturbing to highly disturbing.
Some other drawbacks to this irregularity are that chords and scales employed to produce correct performances are fingered differently from key signature to key signature, and scaling speed suffers in instances where a digit must leap over a black key to link a broken domain pathway.
Finally, the common keyboard does not have the power to use any one of the 12 tonal fingerkeys as the beginning or end of a musical slur executed with one digit. A slur (or grace note) is the rapid sounding of two tones separated by a semitone. On the common keyboard, only the anterior domains of the D, G, and A fingerkeys have a black semitone positioned on both left and right corners. The C and F have a black key to the right, only allowing a descending slur. The B and E have a black key to the left, only allowing an ascending slur. It is impossible to do a one-finger slur to the five black keys themselves, because a finger cannot slam a white key, slide off, and simultaneously jet upwards fast enough to finish up on a black key's top with the correct effect. Jazz artists especially do copius amounts of one-finger slurs for musical expression. Keeping track of multiple slur feasibility arrangements is frustrating to most musicians of the common keyboard.
Although a wholetone arrangement of fingerkeys offers more slur opportunities than a common keyboard, the symmetrical layout causes operators to suffer orientation problems. The use of five landmarked keys of like countenance per octave has been employed. This scheme highlights the five accidentals of the major scale as does the common keyboard.